Drag forces on sparsely packed cube arrays

Flow over aligned and staggered cube arrays is a classic model problem for rough-wall turbulent boundary layers. Earlier studies of this model problem mainly looked at rough surfaces with a moderate coverage density, i.e. O(3%)]]>, where is the surface coverage density and is defined to be the ratio between the area occupied by the roughness and the total ground area. At lower surface coverage densities, i.e. <![CDATA[[STIX]{x1D706}_{p}, it is conventionally thought that cubical roughness acts like isolated roughness elements; and that the single-cube drag coefficient, i.e., equals. Here, is the drag force on one cubical roughness element, is the fluid density, is the height of the cube, is the spatially and temporally averaged wind speed at the cube height, and is the drag coefficient of an isolated cube. In this work, we conduct large-eddy simulations and direct numerical simulations of flow over wall-mounted cubes with very low surface coverage densities, i.e. <[CDATA[0.08%<[STIX] x1D706p. The large-eddy simulations are at nominally infinite Reynolds numbers. The results challenge the conventional thinking, and we show that, at very low surface coverage densities, the single-cube drag coefficient may increase as a function of. Our analysis suggests that this behaviour may be attributed to secondary turbulent flows. Secondary turbulent flows are often found above spanwise-heterogeneous roughness. Although the roughness considered in this work is nominally homogeneous, the secondary flows in our simulations are very similar to those observed above spanwise-heterogeneous surface roughness. These secondary vortices redistribute the fluid momentum in the outer layer, leading to high-momentum pathways above the wall-mounted cubes and low-momentum pathways at the two sides of the wall-mounted cubes. As a result, the spatially and temporally averaged wind speed at the cube height, i.e., is an underestimate of the incoming flow to the cubes, which in turn leads to a large drag coefficient.